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PairwiseGP

As explained in Bayesian Optimization in Action

PairwiseGP is a BoTorch model class for Gaussian-process inference from pairwise comparison data.

PairwiseGP is a BoTorch Gaussian-process model for learning from preferences rather than real-valued observations. Each comparison indicates which of two inputs has the higher latent function value, guiding predictions for Bayesian optimization. section 10.3

A typical training workflow is:

  • Construct PairwiseGP(train_x, train_comp) and evaluate it with PairwiseLaplaceMarginalLogLikelihood, which handles the specialized likelihood of comparisons. section 10.3
  • Fit the marginal log likelihood with fit_gpytorch_mll to obtain the GP posterior that best explains the observed preferences. section 10.3

Interpreting a learned comparison

After observing f(−0.0374) > f(2.6822), the posterior mean favors the first input, while uncertainty decreases around both compared points.

How Bayesian Optimization in Action covers it

How deep it goes
Explains model construction, specialized likelihood fitting, and posterior interpretation, but does not detail the underlying Laplace approximation.
Examples
Uses tensor-encoded inputs and comparisons, including f(−0.0374) > f(2.6822), to illustrate posterior predictions.
What it assumes
Assumes basic Gaussian-process training knowledge and introduces how comparison observations replace ordinary real-valued likelihoods.
What you can do after
Builds and fits a pairwise-comparison GP using BoTorch, then inspects preference-consistent means and reduced predictive uncertainty.
How it connects
Connects Gaussian processes, pairwise comparison data, Bayesian optimization, and Laplace marginal log likelihood.
Cover of Bayesian Optimization in Action
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This explainer was generated by Manning's knowledge graph from the text of Bayesian Optimization in Action. The section links point to the parts of the book it draws on.